Have you tried doing a soft reset on the device? If that does not give you any signs of life, try to put the phone into its Boot Menu by simultaneously pressing the home button, volume up, and power button. If the phone enters the Boot Menu, then try clearing the cache and rebooting it. If the phone does not go into the Boot Menu, then the OS may be corrupt on the device.
If it does, there may be some further hardware issue going on with the device as your buttons are attached to your charging port. Last resort, try wirelessly charging the device. If it powers on, then you know there is an issue with the charge port.